Restricting admissible representations to fixed-point subgroups
| Autor: | Latham, Peter, Nevins, Monica |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given a $p$-adic group $G$ equipped with an action of a finite group $\Gamma\subset\mathrm{Aut}_F(\mathbf{G})$, and a reductive fixed-point subgroup $G^\Gamma$, we establish a relationship between constructions of types for these two groups due to Yu, Kim--Yu and Fintzen, and generalizes the relationship between general linear and classical groups observed by Stevens. As an application, given a parabolically induced or supercuspidal representation $\pi$ of $G$, we explicitly identify a number of the inertial equivalence classes occurring in the representation $\pi|_{G^{[\Gamma]}}$. Comment: 17 pages; Lemma 3.1 corrected; details added to include a missing case |
| Databáze: | arXiv |
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